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These are questions asked by gomez1112

When I tried to solve the following integral, Maple returns it unevaluated. What am I doing wrong?

int(ln(a^2+x^2)/(a^2+x^2)^n, x = 0 .. infinity)


Sum of -(2*((-1)^n-1))*sin(n*Pi*x)*exp(-Pi^2*n^2*t)/(Pi*n) from n=20??? Thank you very much

restart; with(Physics);
Setup(mathematicalnotation = true);
                 [mathematicalnotation = true]
Setup(signature = `-+++`);
                     [signature = - + + +]
Coordinates(M = [t, rho, z, phi]);

  Default differentiation variables for d_, D_ and dAlembertian 

   are: (Mequals(t,ρ,z,φ))
 Systems of spacetime Coordinates are: (Mequals(t,ρ,z,φ))
ds2 := -exp(2*psi(rho, z))*d*(t^2)+exp(2*gamma(rho, z)-2*psi(rho, z))*(drho^2+dz^2)+exp(-2*psi(rho, z))*(rho^2)*(dphi^2);
    ds2 := -exp(2 psi(rho, z)) d t 

                                              /    2     2\
       + exp(2 gamma(rho, z) - 2 psi(rho, z)) \drho  + dz /

                                2     2
       + exp(-2 psi(rho, z)) rho  dphi 
Setup(metric = ds2);
Error, (in Physics:-Setup) expected the metric as an expression quadratic in [d_(t), d_(rho), d_(z), d_(phi)], or square Matrix, Array or table with 4 lines and 4 columns; or a set with the nonzero components of such a matrix; received: -exp(2*psi(rho, z))*d*t^2+exp(2*gamma(rho, z)-2*psi(rho, z))*(drho^2+dz^2)+exp(-2*psi(rho, z))*rho^2*dphi^2

When are we actually going to see the  computation of the Feynman integrals behind the expansion of the Scattering matrix, including dimensional regularization? It’s been at least 5 years since it was mentioned. Thank you.

How can I resolve the following error message? More specifically, how do I set up a coordinate system different from cartesian, spherical, etc in order to pass it to the metric? 



Setup(mathematicalnotation = true);
                 [mathematicalnotation = true]
Setup(signature = `+---`);
                     [signature = + - - -]

ds2 := [(x^2-y^2)*cos(2*u)+2*x*y*sin(2*u)]*(du^2)-2*x*(dv^2)-dx^2-dy^2;
Setup(coordinates = (Z = [u, v, x, y], metric = ds2));
* Partial match of  'coordinates' against keyword 'coordinatesys\

Error, (in Physics:-Setup) expected a list with 4 names, where 4 is the spacetime dimension, or one of the keywords cartesian, spherical, cylindrical; received: ds2

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